Achieving Complete Band Gaps of Water Waves with Shallow-Draft Cylinder Arrays

Abstract

Conventionally, band gaps of water waves can be obtained with periodic arrays of bottom-mounted obstacles or vertical cylinders. However, such structures need to possess a large ratio of volume in water, and may not be easy to build and move in practical ocean engineering. Here, we theoretically propose and experimentally demonstrate that when the water surface is pierced by a fixed, rigid cylinder array, a complete band gap of water waves can be achieved, in which the propagation of water waves is forbidden in all the directions. Such a band gap can exist even when the cylinders have a draft much smaller than the water depth ($d\ensuremath{\ll}h$). Based on the complete band gap, a semicircular shape of the fixed-surface disk array is further constructed, which can block omnidirectional water waves generated by a point source.